The inviscid limit for the 2D Navier-Stokes equations in bounded domains
Claude Bardos, Trinh T. Nguyen, Toan T. Nguyen, Edriss S. Titi
Abstract
<p style='text-indent:20px;'>We prove the inviscid limit for the incompressible Navier-Stokes equations for data that are analytic only near the boundary in a general two-dimensional bounded domain. Our proof is direct, using the vorticity formulation with a nonlocal boundary condition, the explicit semigroup of the linear Stokes problem near the flatten boundary, and the standard wellposedness theory of Navier-Stokes equations in Sobolev spaces away from the boundary.</p>
Topics & Concepts
Inviscid flowBounded functionMathematicsMathematical analysisBoundary (topology)Sobolev spaceNavier–Stokes equationsLimit (mathematics)Domain (mathematical analysis)VorticityBoundary value problemCompressibilityPhysicsVortexClassical mechanicsThermodynamicsNavier-Stokes equation solutionsAdvanced Mathematical Physics ProblemsStability and Controllability of Differential Equations